The variety of nilpotent pairs (A,B) with [A,B] = λI

2025/08/27 by Vlad Roman, Robert M. Guralnick, Roman, Vlad +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2508.20199

openalex publication_date 2025/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be an algebraically closed field of characteristic p >0. We consider the variety of nilpotent pairs (A,B) with [A,B]=λI, namely the set of pairs X = \ (A,B) ∈ M_n(k) × M_n(k) | A,B nilpotent, [A,B]=λI, λ∈ k \. We prove that if n=pr, then X is irreducible of dimension n².

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